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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Nil algebras satisfying an identity of degree three


Author: Raymond Coughlin
Journal: Proc. Amer. Math. Soc. 34 (1972), 63-66
MSC: Primary 17A30
DOI: https://doi.org/10.1090/S0002-9939-1972-0292902-7
MathSciNet review: 0292902
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Abstract: Let A be a nonassociative algebra over a field F with a function $ g:A \times A \times A \to F$ such that $ (xy)z = g(x,y,z)x(yz)$ for all x, y, and z in A. Algebras satisfying this identity have been studied by Michael Rich and the author. It is shown here that a finite-dimensional nil power-associative algebra satisfying the above identity is nilpotent.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0292902-7
Keywords: Power-associative, nil algebra, nilpotent algebra
Article copyright: © Copyright 1972 American Mathematical Society

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